1. Field of the Invention
The present invention relates generally to state estimation processes and, more particularly, to spacecraft subsystems which use such processes.
2. Description of the Related Art
Kalman filtering is an estimation technique that combines a knowledge of the statistical nature of a system's measurement errors with a knowledge of the system's dynamics (as represented, for example, in a state space model) to arrive at an estimate of the system's state. In particular, a Kalman filter combines a current measurement y(t.sub.n) of a system state parameter x(t.sub.n) with measurement and state predictions y*(t.sub.n.sup.-) and x*(t.sub.n.sup.-) of the parameter x(t.sub.n) that are based on past measurements to thereby provide a filtered estimate x*(t.sub.n.sup.+) of the parameter x(t.sub.n). As indicated by the time term t.sub.n, the filter successively and recursively combines the measurements and predictions to obtain estimates with a reduced variance (wherein t.sub.n.sup.- and t.sub.n.sup.+ refer respectively to times just before and after each time t.sub.n).
In an exemplary spacecraft application, a Kalman filter processes attitude and inertial rate measurements to provide an attitude estimate. Although the filter is known to be an especially effective state estimator for these systems, the process tends to have numerical instabilities when it is implemented with digital processors and continued over extensive time periods. The instability has a source in the finite accuracy of digital processing and it represents a danger to long-term spacecraft missions that repeat the same operational mode for years (e.g., as in communication processes of geosynchronous spacecraft). In response to this danger, computationally expensive filter formulations (e.g., Joseph formulation and UDU factorization) have been used to increase numerical stability. These approaches, however, increase the use of processing time which is a limited and tightly budgeted spacecraft resource.
In addition, these stability solutions have a further problem. Because of the high cost of spacecraft missions and the critical nature of spacecraft attitude control systems, it is especially desirable to verify the stability of all such processes over time periods that correspond to those in which the mission will be operational. When these operational time periods are measured in years, such testing is not feasible and, thus, these solutions are not verifiable.